APMA2821N - Notes and Codes


Below are additional notes and Matlab scripts of codes used in class

1. 1/29/12 Class
  1. Harmonic oscillator solver comparison [CODE]
  2. RK system test [CODE]
2. 2/1/12 Class
  1. Convergence of forward Euler for scalar case [CODE]
  2. Convergence of forward Euler for system case [CODE]
  3. Visualization of system case [CODE]
  4. Special case with lower convergence [CODE]
  5. Special case with higher convergence [CODE]

3. 2/15/12 Class
  1. Stability test for scalar forward Euler [CODE]
  2. Stability test for system forward Euler [CODE]
  3. Stability test for system backward Euler [CODE]
  4. Stability region/surface for forward Euler [CODE]
  5. Stability region/surface for backward Euler [CODE]
  6. Backward Euler solved using point iteration [CODE]
  7. Backward Euler solved using a Newton iteration [CODE]
  8. Stability region/surface for Crank-Nicholson [CODE]
  9. Stability region/surface for 2nd order ERK [CODE]
  10. Comparison of schemes for stiff problem [CODE]
  11. Stability region/surface for 2nd order Adam-Bashforth [CODE]
  12. Stability region/surface for 4th order ERK [CODE]

4. 2/29/12 Class
  1. Stability region/surface for 2nd order ERK [CODE]
  2. Stability region/surface for 3rd order ERK [CODE]
  3. Stability region/surface for 4th order ERK [CODE]
  4. Failure of simple RK order condition test [CODE]
  5. Failure of scalar/system RK order conditions [CODE]
  6. Notes on rooted trees [NOTE]

5. 3/7/12 Class
  1. Deformation of 2nd order, 3 stage RK stability region [CODE]
  2. Adaptive ERK code with embedded error estimator [CODE]
  3. Right hand side for gravitational problem [CODE]
  4. Article on limits to stage growth of stability region [NOTE]
  5. Wikipedia page on Pade tables for the exponential [LINK]

6. 3/14/12 Class
  1. Article on limits to stage growth of stability region [NOTE]
  2. Wikipedia page on Pade tables for the exponential [LINK]
  3. Stiff problem and order reduction [CODE]
  4. Right hand side for test problem [CODE]

7. 4/4/12 Class
  1. Stiff problem and order reduction [CODE]
  2. Right hand side for test problem [CODE]

8. 4/11/12 Class
  1. Adam-Bashforth stability regions [CODE]
  2. Adam-Moulton stability regions [CODE]
  3. BDF stability regions [CODE]

9. 4/18/12 Class
  1. Notes on Geometric Integration [NOTE]
  2. Harmonic oscillator solver comparison [CODE]